A block of mass `m` is pushed towards a movable wedge of mass `nm` and height `h`, with a velocity `u`. All surfaces are smooth. The minimum value of `u` for which the block will reach the top of the wedge is

Options

A. `sqrt(2gh)`
B. `n2gh`
C. `sqrt(2gh(1+(1)/(n)))`
D. `sqrt(2gh(1-(1)/(n)))`

Explanation

The centre of mass of the `("block"+"wedge")` must move with speed `=v_(cm)=("mu")/(m+nm)=(u)/(1+n)`
`:. (1)/(2)(m+nm)v_(cm)^(2)=(1)/(2)mu^(2)-mgh`
`rArr (1)/(2)m(1+n)(u^(2))/((1+n^(2)))=(1)/(2)mu^(2)-mgh`
`rArru=sqrt(2gh(1+1//n))`